Geodesic
Comparative analysis of computational methods for periodic transonic flows at low and high frequencies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper presents a comparative analysis via simulation of time-periodic unsteady inviscid flow at low and high frequencies using Time Spectral Method (TSM) and comparing it with the traditional methods such as BDF and Explicit Structured Adaptive Grid Method. The TSM uses a Fourier representation in time. Mathematical tools used here are discrete Fourier transformations. The TSM has been proposed for the fast and efficient computation of periodic unsteady flows. This method has been evaluated and has been validated with NACA pitching airfoils that are widely used and prevalent 2D external aerodynamics test cases. To validate the results presented by the TSM are compared with experimental data and two the other methods. It shows a significant reduction in the computational expense compared to the conventional time-accurate methods, due to taking advantage of the periodic nature of flow by Fourier representation for temporal discretization that has a high accuracy. Also it has shown that TSM can be applied accurately for ample rang of variations of frequency (NACA 64A010 (CT6)) and variations in angle of attacks (NACA 0012 (CT1)). 
@article{ZVMMF_2015_55_12_a10,
     author = {M. R. Mohaghegh and M. Malek-Jafarian},
     title = {Comparative analysis of computational methods for periodic transonic flows at low and high frequencies},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2093},
     year = {2015},
     volume = {55},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a10/}
}
TY  - JOUR
AU  - M. R. Mohaghegh
AU  - M. Malek-Jafarian
TI  - Comparative analysis of computational methods for periodic transonic flows at low and high frequencies
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 2093
VL  - 55
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a10/
LA  - en
ID  - ZVMMF_2015_55_12_a10
ER  - 
%0 Journal Article
%A M. R. Mohaghegh
%A M. Malek-Jafarian
%T Comparative analysis of computational methods for periodic transonic flows at low and high frequencies
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 2093
%V 55
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a10/
%G en
%F ZVMMF_2015_55_12_a10
M. R. Mohaghegh; M. Malek-Jafarian. Comparative analysis of computational methods for periodic transonic flows at low and high frequencies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a10/

[1] L. Schwarz, “Calculation of the pressure distribution of a wing harmonically oscillating in two-dimensional flow”, Luftfahrtforschung, 17:11 (1940), 379 | MR

[2] M. J. Turner, S. Rabinowitz, Aerodynamic coefficients for an oscillating airfoil with hinged flap with tables for a Mach number of 7, NACA Tech. Note, No 2213, 1950, 46 pp.

[3] R. Magnus, H. Yoshihara, “Unsteady transonic flows over an airfoil”, AIAA J., 13:12 (1975), 1622–1628 | DOI

[4] N. H. Kemp, G. Homicz, “Approximate unsteady thin airfoil theory for subsonic flow”, AIAA J., 14:8 (1976), 1083–1089 | DOI | Zbl

[5] E. H. Dowell, S. R. Bland, M. H. Williams, “Linear/nonlinear behavior in unsteady transonic aerodynamics”, 22nd AIAA Structural Dynamics, Material Conference (Atlanta, 1981), AIAA Paper 81-0643, 654–670

[6] B. C. Basu, G. J. Hancock, “The unsteady motion of a two-dimensional airfoil in incompressible inviscid flow”, J. Fluid Mech., 87:1 (1978), 159–178 | DOI

[7] J. Katz, D. Weihs, “Wake rollup, the Kutta condition for airfoils oscillating at high frequency”, AIAA J., 19:12 (1981), 1604–1606 | DOI

[8] W. J. Chyu, S. Davis, K. S. Chang, “Calculation of unsteady transonic flow over an airfoil”, AIAA J., 19:6 (1981), 684–690 | DOI

[9] W. J. McCroskey, “Inviscid flow field of an unsteady airfoil”, AIAA J., 11 (1973), 1130–1137 | DOI | Zbl

[10] W. J. McCroskey, “Unsteady airfoils”, Annu. Rev. Fluid Mech., 14 (1982), 285–311 | DOI | Zbl

[11] R. D. Rausch, H. T. Y. Yang, J. T. Batina, “Euler flutter analysis of airfoils using unstructured dynamic meshes”, J. Aircraft, 27:5 (1990), 436–443 | DOI

[12] J. M. Anderson, K. Streitlien, D. S. Barrett, M. S. Triantafyllou, “Oscillating foils of high propulsive efficiency”, J. Fluid Mech., 360 (1998), 41–72 | DOI | MR | Zbl

[13] S. Mittal, “Finite element computation of unsteady viscous compressible flows”, Comput. Methods Appl. Mech. Eng., 157:1–2 (1998), 151–175 | DOI | MR | Zbl

[14] Z. Yang, L. N. Sankar, M. Smith, O. Bauchau, “Recent improvements to a hybrid method for rotors in forward flight”, 38th AIAA Aerospace Sciences Meeting Exhibit (Reno, NV, January, 2000,), J. Aircraft., 39, no. 5, 2002, 2000-0260, 804–812 | DOI

[15] Q. J. Zhao, G. H. Xu, J. Zhao, “New hybrid method for predicting the flowfields of helicopter rotors”, J. Aircraft, 43:2 (2006), 372–380 | DOI

[16] S. Yang, Z. Zhang, F. Liu, S. Luo, H. M. Tsai, D. Schuster, “Time-domain aeroelastic simulation by a coupled Euler, integral boundary-layer method”, 22nd Applied Aerodynamics Conference Exhibit (Rhode, Island, 2004)

[17] J. M. Hsu, A. Jameson, “An implicit-explicit hybrid scheme for calculating complex unsteady flows”, 40th AIAA Aerospace Sciences Meeting Exhibit (Reno, Nevada, January 14–17, 2002)

[18] S. K. Nadarajah, A. Jameson, “Optimal control of unsteady flows using a time accurate method”, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis, Optimization Conference (Atlanta, GA, September 4–6, 2002), AIAA Paper 2002-5436

[19] J. M. J. Hsu, An implicit-explicit flow solver for complex unsteady flows, Stanford University, 2004, 206 pp.

[20] Z. Zhang, F. Liu, D. M. Schuster, “Calculations of unsteady flow, flutter by an Euler, integral boundary-layer method on Cartesian grids”, 22nd Applied Aerodynamics Conference Exhibit (Rhode Island, 2004)

[21] M. Fard Pasandideh, A. Heidary, M. Malekjafarian, “Numerical analysis of unsteady flow around a oscillator airfoil with moving structured adaptive grid by using central, upwind schemes”, International Aerospace Conference (Ankara, August 17–19, 2009)

[22] K. C. Hall, J. P. Thomas, W. S. Clark, “Computation of unsteady nonlinear flows in cascades using a harmonic balance technique”, 9th International Symposium on Unsteady Aerodynamics, Aeroacoustics, Aeroelasticity of Turbomachines (ISUAAAT) (Lyon, France, September, 2000), AIAA J., 40, no. 5, 2002, 879–886 | DOI

[23] J. P. Thomas, K. C. Hall, E. H. Dowell, “A harmonic balance approach for modeling nonlinear aeroelastic behavior of wings in transonic viscous flow”, AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, Materials Conference, v. 7, 2003, 4779–4784

[24] J. P. Thomas, E. H. Dowell, K. C. Hall, C. M. Denegri, “Further investigation of modeling limit cycle oscillation behavior of the F-16 fighter using a harmonic balance approach”, Collection of Technical Papers: AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, Materials Conference, v. 3, 2005, 1457–1466

[25] J. P. Thomas, C. H. Custer, E. H. Dowell, K. C. Hall, “Unsteady flow computation using a harmonic balance approach implemented about the overflow 2 flow solver”, 19th AIAA Computational Fluid Dynamics Conference (San Antonio, TX, June, 2009), AIAA Paper 2009-4270

[26] M. A. Spiker, J. P. Thomas, R. E. Kielb, K. C. Hall, E. H. Dowell, “Modeling cylinder flow vortex shedding with enforced motion using a harmonic balance approach”, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, Materials (SDM) Conference (Newport, RI, May, 2006), AIAA Paper 2006-1965

[27] L. Liu, J. P. Thomas, E. H. Dowell, P. J. Attar, K. C. Hall, “A comparison of classical, high dimensional harmonic balance approaches for a Duffing oscillator”, J. Comput. Phys., 215:1 (2006), 298–320 | DOI | MR | Zbl

[28] L. Liu, E. H. Dowell, J. P. Thomas, “A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces”, J. Fluids Struct., 23:3 (2007), 351–363 | DOI

[29] A. Da Ronch, M. Ghoreyshi, K. J. Badcock, S. Goertz, M. Widhalm, R. P. Dwight, M. S. Campobasso, “Linear frequency domain, harmonic balance predictions of dynamic derivates”, 28th AIAA Applied Aerodynamics Conference (Chicago, USA, June 28–July 1, 2010)

[30] M. McMullen, A. Jameson, J. J. Alonso, “Application of a nonlinear frequency domain solver to the Euler, Navier–Stokes equations”, AIAA 40th Aerospace Sciences Meeting Exhibit (Reno, NV, 2002), AIAA Paper 02-0120

[31] M. McMullen, A. Jameson, “The computational efficiency of nonlinear frequency domain methods”, J. Comput. Phys., 212 (2006), 637–661 | DOI | Zbl

[32] M. McMullen, A. Jameson, J. J. Alonso, “Demonstration of nonlinear frequency domain methods”, AIAA J., 44:7 (2006), 1428–1435 | DOI

[33] S. Nadarajah, A. Jameson, M. McMullen, “Nonlinear frequency domain based optimum shape design for unsteady three-dimensional flow”, 44th AIAA Aerospace Sciences Meeting Exhibit (Reno, NV, January 9–12, 2006), 2006

[34] S. Nadarajah, A. Jameson, “Optimum shape design for unsteady three-dimensional viscous flows using a NLFD method”, AIAA J. Aircraft, 44:5 (2007), 1513–1527 | DOI

[35] J. S. Cagnone, S. Nadarajah, “An implicit nonlinear frequency domain-spectral difference scheme for periodic Euler flow”, AIAA J., 47:2 (2009), 361–372 | DOI | MR

[36] A. Mosahebi, S. Nadarajah, “Dynamic mesh deformation for implicit adaptive nonlinear frequency domain method”, Seventh International Conference on Computational Fluid Dynamics (ICCFD7) (Big Island, Hawaii, July 9–13, 2012)

[37] A. K. Gopinath, A. Jameson, “Time spectral method for periodic unsteady computations over twoand three-dimensional bodies”, AIAA 43th Aerospace Sciences Meeting Exhibit (Reno, NV, 2005), AIAA Paper 2005-1220, 10683–10696

[38] N. Butsuntorn, A. Jameson, “Time spectral method for rotorcraft flow”, 46th AIAA Aerospace Sciences Meeting Exhibit (Reno, NV, 2008), AIAA Paper 2008-0403

[39] N. Butsuntorn, A. Jameson, “Time spectral method for rotorcraft flow with vorticity confinement”, 26th AIAA Applied Aerodynamics Conference (Honolulu, HI, August 18–21, 2008)

[40] F. Sicot, G. Puigt, M. Montagnac, “Block–Jacobi implicit algorithms for the time spectral method”, AIAA J., 46:12 (2008), 3080–03089 | DOI

[41] A. Jameson, S. Shankaran, “Assessment of dual-time stepping, time spectral, artificial compressibility based numerical algorithms for unsteady flow with applications to flapping wings”, 19th AIAA Computational Fluid Dynamics (San Antonio, Texas, June 22–25, 2009), AIAA Paper 2009-4273

[42] X. Su, X. Yuan, “Implicit solution of time spectral method for periodic unsteady flows”, Int. J. Numer. Methods Fluids, 2009, 860–876 | MR

[43] Z. Yang, D. Mavriplis, “Time spectral method for periodic, quasi-periodic unsteady computations on unstructured meshes”, 40th AIAA Fluid Dynamics Conference (Illinois, June 28–July 1, 2010) | MR

[44] Z. Yang, D. Mavriplis, J. Sitaraman, “Prediction of helicopter maneuver loads using BDF/time spectral method on unstructured meshes”, 49th AIAA Aerospace Sciences Meeting (Florida, January 4–7, 2011)

[45] S. Antheaume, C. Corre, “Implicit time spectral method for periodic incompressible flows”, AIAA J., 49:4 (2011), 791–805 | DOI

[46] A. Jameson, W. Schmidt, E. Turkel, Numerical solutions of the Euler equations by finite volume methods with Runge–Kutta time stepping schemes, AIAA Paper 81-1259, January 1981

[47] A. Jameson, “Transonic flow calculations for aircraft”, Numerical methods in fluid dynamics, Lecture Notes in Mathematics, 1127, Springer, Berlin, 1984, 156–242 | DOI | MR

[48] S. S. Davis, NACA 64A010 (NASA Ames model) oscillatory pitching, AGARD Report 702, AGARD, 2 January 1982

[49] R. H. Landon, NACA 0012 oscillatory, transient pitching, AGARD Report 702, AGARD, 3 January 1982

[50] P. Moin, Spectral methods in computational physics, Supplementary Notes (ME 408), Stanford University, Stanford, CA, 2003 | Zbl